Natural Disasters, When Will They Reach Me?

143 Pages·2016·9.776 MB·English

by  Isuri Wijesundera, Malka N. Halgamuge, Thrishantha Nanayakkara, Thas Nirmalathas (auth.)

Springer Natural Hazards
Isuri Wijesundera
Malka N. Halgamuge
Thrishantha Nanayakkara
Thas Nirmalathas
Natural
Disasters,
When Will They
Reach Me?
Springer Natural Hazards
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More information about this series at http://www.springer.com/series/10179
Isuri Wijesundera Malka N. Halgamuge
(cid:129)
Thrishantha Nanayakkara
Thas Nirmalathas
Natural Disasters, When
Will They Reach Me?
123
Isuri Wijesundera Thrishantha Nanayakkara
MelbourneSchoolof Engineering Department ofInformatics
TheUniversity of Melbourne King’sCollege London
Melbourne, VIC London
Australia UK
Malka N.Halgamuge ThasNirmalathas
Electrical andElectronic Engineering Electrical andElectronic Engineering
TheUniversity of Melbourne TheUniversity of Melbourne
Melbourne, VIC Melbourne, VIC
Australia Australia
ISSN 2365-0656 ISSN 2365-0664 (electronic)
SpringerNatural Hazards
ISBN978-981-10-1111-5 ISBN978-981-10-1113-9 (eBook)
DOI 10.1007/978-981-10-1113-9
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Preface
Predicting natural disasters is extremely important in mitigating disaster related
destructions. In most scenarios, it is equally difficult to predict such events due to
the multitude of factors which affect the formation, propagation and spread of
natural disasters.
Thisbookspecificallyfocusesonpredictingthemeanfirstpassagetimetoreach
a known trigger state for natural disasters modelled as dynamic random processes.
An engineering perspective is followed to describe the prediction methods that
particularly look at random processes which govern natural disaster dynamics that
shows directional dependence and spatial inhomogeneity. Several applications are
referred throughout the book including flood, cyclone and fire predictions.
Someofthematerialpresentedherecanalsobefoundinthefollowingresearch
publications:
1. I. Wijesundera, M.N. Halgamuge, T. Nirmalathas, and T. Nanayakkara (2012),
“A geographic primitive based Bayesian framework to predict cyclone induced
flooding”. Journal of Hydrometeorology, (2012) [1].
2. I. Wijesundera, M.N. Halgamuge, T. Nirmalathas, and T. Nanayakkara (2015),
“Bias modified MFPT prediction for minimal intervention in robotic walkers”,
[Under review].
3. I. Wijesundera, M.N. Halgamuge, T. Nirmalathas, and T. Nanayakkara (2015),
“Meanfirstpassagetimeforcyclonemotionmodelledasbiasedrandomwalks”,
[Under review].
4. I. Wijesundera, M.N. Halgamuge, T. Nirmalathas, and T. Nanayakkara (2015),
“MFPT calculation for random walks in inhomogeneous networks”, [Under
review].
5. I. Wijesundera (2015), “Estimation of mean first passage time (MFPT) in nat-
urally biased inhomogeneous environments”, [PhD Thesis, The University of
Melbourne, Australia, 2015] [2].
Melbourne Isuri Wijesundera
February 2016
vii
viii Preface
References
1. Wijesundera I, Halgamuge MN, Nirmalathas T, Nanayakkara T (2013) Ageographic
primitive-based bayesian framework to predict cyclone-inducedflooding*. J Hydrometeorol
14(2):505–523
2. Wijesundera I H (2015) Estimation of mean first passage time (MFPT) in naturally biased
inhomogeneousenvironments.PhDThesis
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Natural Disasters as Random Walks. . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 The Mean First Passage Time (MFPT) . . . . . . . . . . . . . . 3
1.1.2 Two Common Traits. . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 How to Read This Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Background Guide to Random Walk Analysis . . . . . . . . . . . . . . . . 11
2.1 Introducing Some Basic Notions. . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Random Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Random Walks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.3 Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.4 Random Spread Versus Diffusion . . . . . . . . . . . . . . . . . . 16
2.1.5 Transport Characteristics Describing Random Walks. . . . . 16
2.2 MFPT: A Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Estimating MFPT Using Random Walks’ Transport
Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Analysing the Transition Probability Matrix
to Estimate MFPT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 Random Walks in Natural Disaster Dynamics. . . . . . . . . . 19
2.3 Some Mathematical Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.1 Bayesian Probability Theory. . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 Markov Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.3 Linear Least Square Fitting Technique. . . . . . . . . . . . . . . 24
2.3.4 Monte-Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
ix
x Contents
3 Predicting Cyclone Induced Flood: A Comprehensive
Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Cyclone Activity: One of the Major Forms
of Natural Disasters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Numeric Flood Prediction Models. . . . . . . . . . . . . . . . . . 30
3.2.2 The Concept of Geographic Primitives (GPs). . . . . . . . . . 31
3.2.3 Data Assimilation in Flood Prediction Models . . . . . . . . . 32
3.2.4 Predicting Cyclone Induced Rainfall . . . . . . . . . . . . . . . . 34
3.2.5 Bayesian Theory for Natural Disaster Prediction. . . . . . . . 34
3.2.6 Predicting the Spatial Motion of Cyclones . . . . . . . . . . . . 34
3.3 A Comprehensive Model for Cyclone Induced Flood
Prediction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 Step 1: Predict Cyclone Path with Available Data. . . . . . . 37
3.3.2 Step 2: Predict Rainfall Density Distribution
with Available Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.3 Step 3: Predict Water Deposit Density Distribution
with Available Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Two Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4.1 Model Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Appendix 1: Conversion Between Position and Distance . . . . . . . . . . . 64
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4 First Arrival Time for Natural Disasters Modelled as Biased
Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 Predicting Failure Time Using Transport Variables . . . . . . . . . . . 69
4.2.1 The Fractal Dimension (df) . . . . . . . . . . . . . . . . . . . . . . 69
4.2.2 The Walk Dimension (dw). . . . . . . . . . . . . . . . . . . . . . . 69
4.2.3 Network Exploration by a Random Walk. . . . . . . . . . . . . 70
4.2.4 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3 Time to Reach in Biased Media . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3.1 Simulated Biased Random Walks . . . . . . . . . . . . . . . . . . 72
4.3.2 Calculating Transport Properties for Each NP. . . . . . . . . . 74
4.3.3 Calculating the Walk Dimension (dw) . . . . . . . . . . . . . . . 74
4.4 Case Study: Calculating the Expected Arrival Time for Cyclone
Motion Modelled as Biased Random Walks . . . . . . . . . . . . . . . . 77
4.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4.2 The Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4.3 MFPT Predictions for Case Study. . . . . . . . . . . . . . . . . . 80
4.4.4 Case Study: Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 82